Theorems on the convex hull of an extended real-valued function living on a Hilbert space are presented in case the function is separable and in case the function is a composition of another function and a linear transformation. Equivalence of convex hulls of functions and their biconjugates is used. In particular, it is shown that under properness conditions the biconjugate of a separable func...

We consider a broad class of stochastic dynamic programming problems that are amenable to relaxation via decomposition. These problems comprise multiple subproblems that are independent of each other except for a collection of coupling constraints on the action space. We fit an additively separable value function approximation using two techniques, namely, Lagrangian relaxation and the linear p...

We propose a new p-norm linear discrimination model that generalizes the model of Bennett and Mangasarian (1992) and reduces to linear programming problem with p-order conic constraints. We demonstrate that the developed model possesses excellent methodological and computational properties (e.g., it does not allow for a null separating hyperplane when the sets are linearly separable, etc). The ...

In general the calculation of robustness of entanglement for the mixed entangled quantum states is rather difficult to handle analytically. Using the the convex semidefinite programming method, the robustness of entanglement of some mixed entangled quantum states such as: 2⊗ 2 Bell decomposable (BD) states, a generic two qubit state in Wootters basis, iso-concurrence decomposable states, 2⊗ 3 B...

In this paper, we describe a dynamic programming approach to find optimal trees to the singlesource minimum cost network flow problem with general nonlinear costs. This class of problems is known to be NP-Hard and there is a scarcity of methods to address them. The algorithms previously developed have considered only two particular types of cost functions: “staircase” and “sawtooth”. Here, a dy...

Little-JIL, a new language for programming the coordination of agents is an executable, high-level process programming language with a formal (yet graphical) syntax and rigorously defined operational semantics. Little-JIL is based on two main hypotheses. The first is that the specification of coordination control structures is separable from other process programming language issues. Little-JIL...

Scenario analysis within a multi-stage stochastic programming formulation offers an attractive framework for modelling uncertainties in long-range planning models. However, whether the expected outcome is implicitly / explicitly evaluated, such formulations lead to computationally intensive optimization problems. Focussing here on the scenario planning / multi-period approach for mixed integer ...